After making my snowflake star ornament, I realized that with a little alteration, I could make an ornament that was flat on the back and had the three dimensional points on the front. Even with the stand up points, I still added a gold bead to give the center a more attractive focal point. It also definitely looks better hanging from this orientation.
I pulled out some leftover holly fabric. Instead of starting with 14" strips, I started with 15" strips, just so I wouldn't end up short. Then, instead of folding the strips in half equally, I made the bottom of the fold about an inch shorter than the top:
The shorter strip is used to create the flat back, and the longer one is used to create the three dimensional front.
After creating the three dimensional points, I ended up needing to trim a bit before I tucked, so 14" might have been sufficient, but better safe than sorry: